ANALYSIS OF BOUNDARY LAYER SINGULARITY OF A HYPERBOLIC EQUATION

查看全文 作　　者：ZHANG Weitao;FENG Dexing Institute of Systems Science, Academia Sinica, Beijing 100080, China 出　　处：《Systems Science and Mathematical Sciences》索引1993年第6卷第4期,共11页 基　　金：This research is supported by the National Natural Science Foundation of China. 摘　　要：Using the interpolation theory of a family of linear operators and the Sobolevspaces, we introduce a quantity J_∈~4(λ) which depicts the shape of the boundary layer, andthen analyze the boundary singularty of J_∈~4(λ). Our result shows that the thickness of theboundary layer (or the regular region of J_∈~4(λ)) is intrinsically related to the reciprocal ofthe order of the equation; the loss of boundary conditions between the singular solution andthe limit solution does not influence the thickness of the boundary layer, but it influencesthe process of increasing singularity of J_∈~4(λ); the more the loss of boundary conditions, thesmaller the region of increasing singularity. Finally, we give a definition of a neighborhoodof sudden change and propose an open problem regarding this neighborhood. 关 键 词：The INTERPOLATION theory the INTERIOR estimate the boundary layer SINGULARITY the NEIGHBORHOOD of SUDDEN change